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A remark on a helicopter and submarine game
Author(s) -
Garnaev Andrej Y U.
Publication year - 1993
Publication title -
naval research logistics (nrl)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.665
H-Index - 68
eISSN - 1520-6750
pISSN - 0894-069X
DOI - 10.1002/1520-6750(199308)40:5<745::aid-nav3220400514>3.0.co;2-1
Subject(s) - mathematics , integer (computer science) , combinatorics , point (geometry) , zero sum game , position (finance) , stochastic game , discrete mathematics , mathematical economics , computer science , game theory , geometry , finance , programming language , economics
The article considers a two‐person zero‐sum game in which the movement of the players is constrained to integer points …, −1, 0, 1, … of a line L. Initially the searcher (hider) is at point x = 0 ( x = d, d > 0). The searcher and the hider perform simple motion on L with maximum speeds w and u , respectively, where w > u > 0. Each of the players knows the other's initial position but not the other's subsequent positions. The searcher has a bomb which he can drop at any time during his search. Between the dropping of the bomb and the bomb exploding there is a T time lag. If the bomb explodes at point i and the hider is at point i − 1, or i , or i + 1, then the destruction probability is equal to P , or 1, or P , respectively, where 0 < P < 1. d, w, u , and T are integer constants. The searcher can drop the bomb at integer moments of time t = 0, 1, … . The aim of the searcher is to maximize the probability of the destruction of the hider. © 1993 John Wiley & Sons, Inc.